## Restricted Access

**Reason:** Access restricted by the author. A copy can be requested for private research and study by contacting your institution's library service. This copy cannot be republished

# Volatility in the black-scholes and other formulas

thesis

posted on 2017-03-22, 01:26 authored by Mah, OliviaThis thesis examines the compatibility between the Black-Scholes formula and stock price models with non-constant implied volatility. Our implied volatility is assumed to be a (possibly random) function of time t. Our main result shows that if the price of a call option is given by the Black-Scholes formula for finitely many strike prices, then the implied volatility is not necessarily a constant but will approach a constant if the number of strike prices increases. Moreover, our results provide us with sets of constraints limiting the acceptable values of the implied volatility parameters. We show that the more maturities we have, the more refined our constraints on the implied volatility would be. Since we do not place any assumptions on the underlying stock price process, the implied volatility process or how they are related, our results are model-free.
In addition, we extend our investigation on the compatibility issue by using a more general formula than the Black-Scholes for our implied volatility. Under this more general framework, we obtain the same conclusion, namely, that implied volatility is not necessarily a constant but will approach a constant if the number of strike prices increases. We show this for the cases of
three maturities and multiple maturities.

## History

## Campus location

Australia## Principal supervisor

Fima Klebaner## Year of Award

2011## Department, School or Centre

Mathematics## Course

Doctor of Philosophy## Degree Type

DOCTORATE## Faculty

Faculty of Science## Usage metrics

## Categories

No categories selected## Keywords

## Licence

## Exports

RefWorks

BibTeX

Ref. manager

Endnote

DataCite

NLM

DC